Problem: Factor completely. $25x^2-16=$
Solution: Both $25x^2$ and $16$ are perfect squares, since $25x^2=({5x})^2$ and $16=({4})^2$. $25x^2-16 = ({5x})^2-({4})^2$ So we can use the difference of squares pattern to factor. ${a}^2 - {b}^2 =({a}+{b})({a}-{b})$ In this case, ${a}={5x}$ and ${b}={4}$ : $({5x})^2 - ({4})^2 =({5x}+{4})({5x}-{4})$ In conclusion, $25x^2-16=(5x+4)(5x-4)$ Remember that you can always check your factorization by expanding it.